Systems of correlation functions, coinvariants and the Verlinde algebra

Details Systems of correlation functions, coinvariants and the Verlinde algebra Systems of correlation functions, coinvariants and the Verlinde algebra

2010-03-15

arxiv.org/abs/1003.2949v2

Mathematics

Representation Theory

17 pages

Scientific paper

We study the Gaberdiel-Goddard spaces of systems of correlation functions attached to an affine Kac-Moody Lie algebra $\gh$. We prove that these spaces are isomorphic to the spaces of coinvariants with respect to certain subalgebras of $\gh$. This allows to describe the Gaberdiel-Goddard spaces as direct sums of tensor products of irreducible $\g$-modules with multiplicities given by fusion coefficients. We thus reprove and generalize Frenkel-Zhu's theorem.

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